Transmission of a Bit Over a Discrete Poisson Channel With Memory

DOI10.1109/TIT.2021.3077872zbMATH Open1475.94064arXiv2011.05931OpenAlexW3159324521MaRDI QIDQ5001821

Niloufar Ahmadypour, Amin Gohari

Publication date: 23 July 2021

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: A coding scheme for transmission of a bit maps a given bit to a sequence of channel inputs (called the codeword associated to the transmitted bit). In this paper, we study the problem of designing the best code for a discrete Poisson channel with memory (under peak-power and total-power constraints). The outputs of a discrete Poisson channel with memory are Poisson distributed random variables with a mean comprising of a fixed additive noise and a linear combination of past input symbols. Assuming a maximum-likelihood (ML) decoder, we search for a codebook that has the smallest possible error probability. This problem is challenging because error probability of a code does not have a closed-form analytical expression. For the case of having only a total-power constraint, the optimal code structure is obtained, provided that the blocklength is greater than the memory length of the channel. For the case of having only a peak-power constraint, the optimal code is derived for arbitrary memory and blocklength in the high-power regime. For the case of having both the peak-power and total-power constraints, the optimal code is derived for memoryless Poisson channels when both the total-power and the peak-power bounds are large.

Full work available at URL: https://arxiv.org/abs/2011.05931

zbMATH Keywords

discrete Poisson channel with memorypeak-power and total-power constraints

Mathematics Subject Classification ID

Channel models (including quantum) in information and communication theory (94A40) Coding theorems (Shannon theory) (94A24)

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